For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.
Dusart,Estimates of some functions over primes without R.H
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
Some computations made about the Riemann Hypothesis and in particular, the verification that zeroes of zeta belong on the critical line and the extension of zero-free region are useful to get better effective estimates of number theory classical functions which are closely linked to zeta zeroes like psi(x), theta(x), pi(x) or the k-th prime number.
years
2026 4representative citing papers
Fixed-architecture networks of width O(D) and depth O(r) approximate Hölder functions with parameter magnitude log P = O(ε^{-2D/(r+γ)} log(1/ε)) via CRT encoding.
The vertex-coloring coprime Ramsey number R_cop(k1,...,kc) equals the prime p indexed by sum(ki-1).
For large primes p, the least consecutive pair of primitive roots u and u+1 (u not ±1 or a square) satisfies u ≪ O((log p)^2 (log log p)^5).
citing papers explorer
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A Complete Answer to Erd\H{o}s Problem 690
For every k ≥ 4 the map p to the natural density of integers whose k-th smallest prime divisor is p fails to be unimodal.
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On Explicit Super-Expressive Approximation for Neural Networks
Fixed-architecture networks of width O(D) and depth O(r) approximate Hölder functions with parameter magnitude log P = O(ε^{-2D/(r+γ)} log(1/ε)) via CRT encoding.
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Prime Certificates for Exact Vertex-Coprime Ramsey Numbers
The vertex-coloring coprime Ramsey number R_cop(k1,...,kc) equals the prime p indexed by sum(ki-1).
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Least Consecutive Pair of Primitive Roots
For large primes p, the least consecutive pair of primitive roots u and u+1 (u not ±1 or a square) satisfies u ≪ O((log p)^2 (log log p)^5).